Geometric topology of spaces with curvature bounded above

• Project/Area Number: 21740036
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: University of Tsukuba
• Principal Investigator: NAGANO Koichi 筑波大学, 数理物質系, 講師 (30333777)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 幾何学 / CAT(0)空間 / アダマール空間 / アレキサンドルフ空間 / CAT(1)空間

Research Abstract

For spaces with curvature bounded above, especially CAT(k) spaces, I have aimed to unite the metric geometry with the geometric topology. As joint works with Lytchak, I have mainly tried to study the wall type singularity of CAT(k) spaces, the polyhedral local topological regularity of CAT(k) spaces, and the asymptotic topological regularity of CAT(0) spaces, and obtain several versatile results.

Research Products

• [Presentation] CAT(0)空間に対する漸近的位相正則性 (2012)
  • Author(s): 永野 幸一
  • Organizer: 筑波大学微分幾何学火曜セミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2012-12-04
• [Presentation] Wall type singularity of spaces with anupper curvature bound (2011)
  • Author(s): 永野 幸一
  • Organizer: 研究集会「リーマン幾何学と幾何解析」
  • Place of Presentation: 筑波大学
  • Year and Date: 2011-02-19
• [Presentation] Wall type singularity of spaces with an upper curvature bound (2011)
  • Author(s): 永野幸一
  • Organizer: 研究集会「リーマン幾何学と幾何解析」
  • Place of Presentation: 筑波大学
  • Year and Date: 2011-02-19
• [Presentation] Wall type singularity of spaces with anupper curvature bound (2010)
  • Author(s): 永野 幸一
  • Organizer: The 2010 General Topology Symposium
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-12-21
• [Presentation] 曲率が上に有界な空間の壁型特異性 (2010)
  • Author(s): 永野 幸一
  • Organizer: 筑波大学微分幾何学火曜セミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-11-09
• [Presentation] Wall type singularity of spaces with anupper curvature bound (2010)
  • Author(s): Koichi Nagano
  • Organizer: The 6^<th> Geometry Conference for Friendship of China and Japan
  • Place of Presentation: 西北大学(西安,中国)
  • Year and Date: 2010-09-05
• [Presentation] Wall type singularity of spaces with an upper curvature bound (2010)
  • Author(s): Koichi Nagano
  • Organizer: The 6^<th> Geometry Conference for Friendship of China and Japan
  • Place of Presentation: 西北大学(西安,中国)(招待講演)
  • Year and Date: 2010-09-05
• [Presentation] Geodesically complete spaces with an uppercurvature bound (2010)
  • Author(s): 永野 幸一
  • Organizer: 名古屋大学 学生プロジェクト 幾何学セミナー
  • Place of Presentation: 名古屋大学
• [Presentation] Geodesically complete spaces with an upper curvature bound (2010)
  • Author(s): 永野幸一
  • Organizer: 名古屋大学学生プロジェクト幾何学セミナー
  • Place of Presentation: 名古屋大学
• [Book] 曲率が上に有界なホモロジー多様体,大学院GP数学レクチャーノートシリーズ,14,東北大学大学院理学研究科 (2010)
  • Author(s): 永野 幸一